Factor Trinomials Game
This game will challenge you to factor a trinomial.
You can select whether to work with trinomials where the leading coefficient is 1 or where the leading coefficient is greater than 1.
If the leading coefficient (a) of the trinomial is 1, find two numbers that multiply to the constant (c) and add to the middle coefficient (b) to form two binomials.
If (a) is greater than 1, use the “AC method”: multiply ‘a’ and ‘c’, find two numbers that multiply to ‘ac’ and add to ‘b’, replace ‘bx’ with these two numbers, and then factor by grouping. Scroll down the page for a more detailed explanation.
If you get an answer wrong, the game will show you the correct solution.
 

 

How to Play the Factor Trinomials Game
The game will challenge you to multiply two binomials and provide the resulting trinomial.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given a trinomial. Factor it.
   
3. Enter Your Answer: Enter in the coefficients for x and the constant. Remember to enter the negative symbol for negative numbers.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

Factoring Trinomials with a Leading Coefficient of 1 (a=1)
A trinomial in the form x² + bx + c can be factored by finding two numbers that:

1. Multiply to the constant term, c.
   Add up to the coefficient of the middle term, b.
   Example: Factor x² + 5x + 6.
   
2. Find two numbers that multiply to 6 (c) and add to 5 (b).
   The numbers 2 and 3 satisfy these conditions (2 × 3 = 6 and 2 + 3 = 5).
   Therefore, the factored form is (x + 2)(x + 3).
    
   

Factoring Trinomials with a Leading Coefficient Greater Than 1 (a > 1)
For a trinomial in the form ax² + bx + c where a > 1, use the “AC Method” and factor by grouping.

1. Find the product ac: Multiply the leading coefficient (a) by the constant term (c).
   
2. Find two numbers: Find two numbers that multiply to the product ac and add to the middle coefficient, b.
   
3. Rewrite the middle term: Replace the bx term with the two numbers you found, written as px + qx. The trinomial is now ax² + px + qx + c.
   
4. Factor by grouping: Group the first two terms and the last two terms, and factor out the greatest common factor (GCF) from each group.
   
5. Check the result: The two factored groups should be identical, allowing you to write the final factored form.
    
   Example: Factor 6z² + 11z + 4.
   a = 6, b = 11, c = 4.
   ac = 6 × 4 = 24 .
   Find two numbers that multiply to 24 and add to 11. These numbers are 8 and 3 (8 × 3 = 24 and 8 + 3 = 11).
   Rewrite the middle term: 6z² + 8z + 3z + 4.
   Factor by grouping: (6z² + 8z) + (3z + 4).
   Factor out the GCF from each group: 2z(3z + 4) + 1(3z + 4).
   Final factored form: (2z + 1)(3z + 4).
    
   

The video gives a clear, step-by-step approach to factor trinomials where a = 1.

• Show Video

The video gives a clear, step-by-step approach to factor trinomials where a > 1.

• Show Video

 

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